Pk. Monteiro et Fh. Page, Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints, J MATH ECON, 30(4), 1998, pp. 473-502
We analyze the nonlinear pricing problem faced by an incomplete information
monopolist operating in a market populated by agents with budget constrain
ts. We show that if other goods are available and if the monopolist's goods
are nonessential relative to other goods, then there exists an optimal, in
dividually rational, and incentive compatible selling mechanism for the mon
opolist (Theorem 1). Moreover, we show that a solution to all such nonlinea
r pricing problems exists if and only if the monopolist's goods are nonesse
ntial (Theorem 2). In the absence of nonessentiality, we show that if the m
onopolist's profit function is independent of quantity (e.g., if all costs
are fixed), then an optimal selling mechanism exists (Theorem 3). Finally,
we show that if there is reporting (of types by agents) and partial recogni
tion of types (by the monopolist), then an optimal selling mechanism exists
, even in the absence of nonessentiality, provided agents' utility function
s are affine and continuous in goods (Theorem 4). (C) 1998 Elsevier Science
S.A. All rights reserved. JEL classification: C72; D82; D42.